Tiffany is 3 times as old as Ben. Twenty years ago, Tiffany was 7 times as old as Ben. How old is Tiffany now?
Answer: We can use the given information to write down two equations that describe the ages of Tiffany and Ben. Let Tiffany's current age be $t$ and Ben's current age be $b$ The information in the first sentence can be expressed in the following equation: $t = 3b$ Twenty years ago, Tiffany was $t - 20$ years old, and Ben was $b - 20$ years old. The information in the second sentence can be expressed in the following equation: $t - 20 = 7(b - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $t$ , it might be easiest to solve our first equation for $b$ and substitute it into our second equation. Solving our first equation for $b$ , we get: $b = t / 3$ . Substituting this into our second equation, we get: $t - 20 = 7($ $(t / 3)$ $- 20)$ which combines the information about $t$ from both of our original equations. Simplifying the right side of this equation, we get: $t - 20 = \dfrac{7}{3} t - 140$ Solving for $t$ , we get: $\dfrac{4}{3} t = 120$ $t = \dfrac{3}{4} \cdot 120 = 90$.